A weak lift pump will first show up on the Cummins B-series engines as extended cranking. It should start in 1 to 2 revolutions of the crankshaft. If it takes 2-3 seconds to fire, the lift pump is weak. If it takes more than 5 seconds, order a new lift pump.
I chased starting problems on a 4BT this winter. Long crank, replaced inline fuel filter. Hard to bleed, and eventually no fuel to the injectors - shutoff valve on Bosch injector pump stuck closed. Replaced the shutoff valve - wouldn't shut off! - new valve would hang open in random positions. Second new shutoff valve - no fuel delivered - replaced lift pump - new pump not fully machined, so outlet line wouldn't seat. Second new lift pump worked well, Now it starts in one crankshaft revolution.
I have a 12 Volt automotive fuel pump I've rigged up with an inline filter. I attach it to my inline fuel filter, crack the vent at the injector pump, and fill the system until I get no air bubbles from the bleeder, pumping from a gallon can of clean fuel.